self-contained, serverless,
zero-configuration, transactional SQL
database engine. SQLite is easily the most
broadly used SQL database engine in
the planet. The origin code for SQLite
is incorporated in the public domain.

Firebird is definitely an free relational
database offering many ANSI SQL-99
features that operates on Linux, Home windows,
and a number of Unix platforms.
Firebird offers excellent concurrency,
high end, effective language
support for saved methods and
triggers.

Unsure it meets no install requirement but when you'll need a lot more than SQLite check Apache Derby.

If you are employed in Java, HSQLSB may well be a good fit. Otherwise, SQLite.

Tokyo, japan Cabinet will be a good candidate, except it is not relational (so no SQL).
Given you do not have a lot of records, perhaps a full relational database is overkill to your requirements. Or otherwise, it is dependent in your application, obviously.